Related papers: Categorical Schr\"odinger Bridge Matching

Stochastic neural networks such as Restricted Boltzmann Machines (RBMs) have been successfully used in applications ranging from speech recognition to image classification. Inference and learning in these algorithms use a Markov Chain Monte…

Markov state models (MSMs) are valuable for studying dynamics of protein conformational changes via statistical analysis of molecular dynamics (MD) simulations. In MSMs, the complex configuration space is coarse-grained into conformational…

We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…

We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of…

Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…

The Schr\"odinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport…

This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…

The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have…

Generative models offer a direct way of modeling complex data. Energy-based models attempt to encode the statistical correlations observed in the data at the level of the Boltzmann weight associated with an energy function in the form of a…

Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main…

Computational methods for learning to sample from the Boltzmann distribution -- where the target distribution is known only up to an unnormalized energy function -- have advanced significantly recently. Due to the lack of explicit target…

Molecular Dynamics (MD) is crucial in various fields such as materials science, chemistry, and pharmacology to name a few. Conventional MD software struggles with the balance between time cost and prediction accuracy, which restricts its…

A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…

A principled approach to characterize the hidden structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for…

This work introduces a novel nonlinear optimal filtering method, termed the Ensemble Schr{\"o}dinger Bridge nonlinear filter. The proposed filter combines the standard prediction step with a diffusion-generative-modeling-based analysis…

Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an…

Continuous-time Bayesian networks (CTBNs) are graphical representations of multi-component continuous-time Markov processes as directed graphs. The edges in the network represent direct influences among components. The joint rate matrix of…

There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…

In this paper, we present structured message passing (SMP), a unifying framework for approximate inference algorithms that take advantage of structured representations such as algebraic decision diagrams and sparse hash tables. These…

This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schroedinger equation. Adding an Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently…